Fano manifolds having (n-1,0)-type extremal rays with large Picard number

Abstract

We classify smooth Fano manifolds X with the Picard number ${\rho }_X\ge 3$ such that there exists an extremal ray which has a birational contraction that maps a divisor to a point.

arXiv comment10 pages

References in corpus (1)

• Variétés projectives complexes dont l'éclatée en un point est de Fano

Cited by in corpus (6)

• On K-stability and the volume functions of $\mathbb{Q}$-Fano varieties
• On the second and third exterior power of tangent bundles of Fano manifolds with birational contractions
• Fano manifolds containing a negative divisor isomorphic to a rational homogeneous space of Picard number one
• Towards a criterion for slope stability of Fano manifolds along divisors
• Positivity of the second exterior power of the tangent bundles
• Extremal contractions of 2-Fano fourfolds